Are you sure you've transcribed the question correctly? And please remember to include the SOURCE of the question! As written, this is not very GMAT-like. It's too open to interpretation, and is not very real-world realistic.

Question: how many hours did Suresh travel yesterday?

(1) Yesterday, Suresh traveled from 1 A.M. to 1P.M. without a break.
Ok, this tells us that he traveled for 12 hrs, so it seems sufficient... but what if he took a break from 1-3pm, then resumed traveling? The total could be more than 12. Insufficient.

(2) Yesterday, Suresh traveled half the total number of hours he traveled the day before yesterday.
The day before tells us nothing about yesterday, as we're given no actual value. Insufficient.

1 & 2 Together:
Yesterday he traveled at least 12 hours... but he also traveled some amount that was half of the previous day's time. Since there are only 24 hrs in a day, the maximum number of hours he could have traveled yesterday is 12.Sufficient.

So, we can get to C by thinking it through in this way, though I've never seen an official GMAT question employ exactly this kind of trick: "I told you that he traveled these 12 hrs, but I didn't tell you if those were the only hours he traveled."

What's the source of this question?